GW170817 Measured the Hubble Constant With No Ladder

Chapters

1. 0:00 Two neutron stars and no ladder
2. 0:32 The ladder it skips
3. 1:47 17 August 2017
4. 2:08 What the detectors recorded
5. 3:16 The chirp mass
6. 4:12 The tilt problem
7. 6:10 The distance, from the wave alone
8. 7:03 The speed of the galaxy
9. 8:00 Speed over distance
10. 8:52 What it settles, and what it does not
11. 9:45 Measuring the tilt another way
12. 11:41 The number that was measured

Transcript

Two neutron stars and no ladder 0:00

Two neutron stars collided in two thousand seventeen, and measured the Hubble constant with no ladder. A gravitational wave gave the distance. A galaxy gave the speed. The answer was seventy, with a wide margin on either side.

We recomputed the climb of that wave from the published mass, and it starts at twenty four hertz a hundred seconds out, as the paper says. This episode asks how wide the margin is, and which single angle sets it.

The ladder it skips 0:32

The last two episodes climbed a ladder. Parallax, then Cepheid stars, then supernovae, each rung calibrated on the one below, and each inheriting the error beneath it. A distance from a gravitational wave does not touch any of those rungs.

In nineteen eighty six, Bernard Schutz proposed it. Two neutron stars spiralling together send out a wave whose shape depends on their masses, and whose strength depends on the distance. His estimate: ten events out to a hundred megaparsecs might fix the Hubble constant to three per cent.

The name came nineteen years later. In two thousand five, Daniel Holz and Scott Hughes called such a source a standard siren, the gravitational wave counterpart of a standard candle. A siren is judged by how loud it is. That is the whole method.

A standard candle is judged by its brightness, and that brightness has to be known from somewhere else: a rung below. A siren needs no rung. Its strength at the source is predicted by general relativity from the shape of the wave itself, and the distance falls out of the comparison.

17 August 2017 1:47

On the seventeenth of August, two thousand seventeen, at forty one minutes past twelve, universal time, three detectors recorded a signal. Two LIGO sites, in Hanford and Livingston, and Virgo, in Italy. It was the loudest gravitational wave signal found up to then.

What the detectors recorded 2:08

What a detector returns is not a distance, and not a brightness. It is a strain: how much the arms of the interferometer stretch and squeeze, as a fraction of their length. For this event, a fraction of the order of ten to the minus twenty two.

Each detector is an interferometer. Laser light runs down two perpendicular arms, and a passing wave changes the phase difference between the two beams. That phase difference is the raw reading. Strain, the stretch as a fraction of the arm, is what is worked out from it.

And the signal was long. Counted from twenty four hertz, it stayed in the sensitive band for about a hundred seconds, climbing in pitch the whole time. Most earlier signals had lasted a few seconds.

This is that climb. It is not the detector data. It is the curve the published mass predicts, in the last ten seconds, at real speed: fifty seven hertz at the start, over seven hundred in the last hundredth of a second.

The chirp mass 3:16

How fast the pitch climbs is set by one combination of the two masses, called the chirp mass. For this event it came out at one point one eight eight times the mass of the sun, good to a few thousandths. Notice what that needed: a rate of change. No distance.

The individual masses are less certain. The chirp mass is the one combination the signal fixes tightly. How the total splits between the two stars is blurred by how fast each one spins. The distance needs only the chirp mass, and that is a stroke of luck.

With the masses known, general relativity says how strong the wave was at the source. The detectors measured how strong it was here. The weaker it arrived, the farther it came. No star's brightness enters the sum, and no ladder.

The tilt problem 4:12

But the strength of the wave depends on a second thing: how the orbit is tilted toward us. A binary seen face on, far away, makes a wave about as strong as one seen edge on, closer in. From amplitude alone, distance and tilt cannot be told apart.

That is why the third detector mattered. Two LIGO sites that nearly line up measure the polarization of the wave poorly, and polarization is what carries the tilt. With Virgo, the cosine of the tilt was held between minus one and minus point eight one.

The paper lists three sources for the fifteen per cent uncertainty in the distance. Noise in the detectors. The calibration of the instruments. And a geometric factor, the correlation of distance with tilt. The first two belong to the instruments. The third belongs to the orbit.

Three detectors also say where to look. Two give a patch of a hundred and ninety square degrees. With Virgo, twenty eight. A patch that size holds many galaxies, and the next hours decided which one was the source.

Within eleven hours, a one metre telescope found a new point of light, in a galaxy called NGC forty nine ninety three. A gamma ray burst had already arrived one point seven seconds after the merger. The chance that the light and the galaxy line up by accident is four thousandths of one per cent.

This is the part Schutz's original proposal did not need. It did not rely on identifying the host galaxy of a single event. Here the light did: it named NGC forty nine ninety three, and a named galaxy has a speed. Without the light there is a distance, and nothing to divide it by.

The distance, from the wave alone 6:10

Now fix the sky position at that light, and read the distance from the wave alone: forty three point eight megaparsecs, about a hundred and forty three million light years, with a margin of plus two point nine and minus six point nine.

The first paper had left the sky position free, and got forty, plus eight, minus fourteen. Same data, different assumption. A distance from the galaxy's light, which does lean on the ladder, gave forty one point zero, plus or minus three point one. It agrees.

At three thousand kilometres per second, a galaxy moves at about one per cent of the speed of light. That is slow enough for the simplest law to hold: speed equals the Hubble constant times distance. Nothing relativistic needs to be corrected.

The speed of the galaxy 7:03

That is half the ratio. The other half is speed, and the speed is the easy half. NGC forty nine ninety three belongs to a group of galaxies, and the group recedes at three thousand three hundred and twenty seven kilometres per second, plus or minus seventy two, measured against the cosmic microwave background.

But galaxies are also pulled. The whole region is streaming toward a mass concentration called the Great Attractor, and that flow is worth about three hundred and ten kilometres per second. Subtract it: three thousand and seventeen.

The team did not trust that correction to its own stated precision. They adopted one hundred and fifty kilometres per second for the uncertainty on the flow, and the speed became three thousand and seventeen, plus or minus one hundred and sixty six. That is five and a half per cent.

Speed over distance 8:00

Speed over distance. Three thousand and seventeen divided by forty three point eight is sixty eight point nine. That is where the peak should sit, and the paper says so. The published best value is seventy point zero.

The gap is not an error. A ratio of two peaks is not the peak of the result, because the full calculation weighs the whole probability curve. And that curve is lopsided: its median is seventy four, plus sixteen, minus eight. There are three honest ways to read one curve.

The paper's number is seventy point zero, plus twelve, minus eight, in kilometres per second for every megaparsec. At sixty eight per cent credibility, that runs from sixty two to eighty two.

What it settles, and what it does not 8:52

Planck predicts sixty seven point four. The Hubble ladder measured seventy three. Both sit inside the interval. The paper says so itself: the measurement does not resolve the tension, and is broadly consistent with both.

The margin averages ten units. The Hubble ladder's is a little over one, and Planck's is a half. So this first siren is about ten times looser than the ladder, and twenty times looser than Planck. What it offers is not precision. It is independence.

No Cepheid went into that number. No supernova, no parallax, no anchor galaxy. Whatever is wrong with the ladder, if anything is, cannot be wrong here. What can be wrong here is the model of the tilt.

Measuring the tilt another way 9:45

So astronomers measured the tilt another way, with radio telescopes. Over the months after the merger, a compact radio source appeared to move faster than light. A jet can do that when it points fairly close to us. The motion implies a narrow jet, seen from about twenty degrees.

Those radio images came from very long baseline interferometry, the technique behind the black hole portraits, at two moments: seventy five days and two hundred and thirty days after the merger. Between them the source moved, and the jet's opening came out under five degrees.

Feed that angle back, and the distance stops being tied to the tilt. The margin shrinks from fourteen per cent to about seven. The published value is seventy point three, plus five point three, minus five. The preprint of the same analysis says sixty eight point nine.

Other groups fitted the same two stars differently. With the kilonova, the afterglow and a model of neutron star matter: sixty six point two. With the late afterglow and a wider viewing angle: seventy two point six. With the afterglow followed for three and a half years: seventy five point five.

One collision, one wave, and the answer runs from sixty six to seventy five. The spread is about twice as wide as the margin each of them claims. The tilt was the uncertainty in the first paper, and a choice of model in every paper since.

Schutz estimated ten events. The first one gave fourteen per cent. A single siren cannot decide between sixty seven and seventy three. It can only add one independent vote, and say how loud it was.

The number that was measured 11:41

Which leaves the number this episode ends on. Not the distance, and not the speed. What the detectors returned was a strain, of the order of ten to the minus twenty two. Every number after it was converted, and one of the conversions was the tilt.

The Hubble constant from the sound of two neutron stars: seventy, plus twelve, minus eight kilometres per second for every megaparsec. Fourteen per cent, with no ladder.

Next time, a supernova seen three times. Webb found one explosion whose light reached us by three paths, up to a hundred and sixteen days apart, and the delays gave seventy five point seven, plus eight point one, minus five point five.

Description and sources

A gravitational-wave detector does not return a distance. It returns a strain, of the order of one part in ten to the twenty-two, for about a hundred seconds. How fast the pitch climbs fixes the chirp mass, 1.188 solar masses for GW170817, with no distance in it. General relativity then says how strong the wave was at the source, and the detectors measured how strong it was here: that ratio is a luminosity distance, 43.8 megaparsecs with the sky position fixed on NGC 4993. The catch is the tilt of the orbit, which a face-on binary far away and an edge-on binary closer in share. Add the galaxy group's recession speed, 3017 +/- 166 kilometres per second, and the division gives a Hubble constant of 70.0 +12.0/-8.0, with a 68 per cent interval from 62 to 82. It agrees with Planck's 67.4 and with the 73 of the Hubble ladder, and settles nothing between them. What it offers is independence: no Cepheid, no supernova, no anchor galaxy. Later groups fixed the tilt with radio jets, kilonova models and the afterglow, and got 66.2 to 75.5 from the same two stars.

PRINT-READY, FROM THIS CHANNEL

The Conversion Chain, Vol. 01 — the method, and four numbers taken apart with it

https://therepository.gumroad.com/l/the-conversion-chain

PRIMARY SOURCES

• LIGO Scientific Collaboration and Virgo Collaboration et al. (2017). A gravitational-wave standard siren measurement of the Hubble constant. Nature 551, 85; arXiv:1710.05835 -- H0 = 70.0 +12.0/-8.0 (maximum a posteriori, 68%); median 74.0 +16/-8; distance 43.8 +2.9/-6.9 Mpc; Hubble velocity 3017 +/- 166 km/s; NGC 4993; Tully-Fisher check 41.1 +/- 5.8 Mpc.
• Abbott, B. P. et al. (2017). GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral. PRL 119, 161101; arXiv:1710.05832 -- chirp mass 1.188 +0.004/-0.002 solar masses; about 100 s from 24 Hz; strain of order 1e-22; 28 deg2 with three detectors; distance 40 +8/-14 Mpc; gamma-ray burst 1.7 s after.
• Abbott, B. P. et al. (2017). Multi-messenger Observations of a Binary Neutron Star Merger. ApJL 848, L12; arXiv:1710.05833 -- SSS17a / AT 2017gfo in NGC 4993, less than 11 hours after the merger.
• Hjorth, J. et al. (2017). The Distance to NGC 4993. ApJL 848, L31; arXiv:1710.05856 -- 41.0 +/- 3.1 Mpc.
• Schutz, B. F. (1986). Determining the Hubble constant from gravitational wave observations. Nature 323, 310 -- the method; ten events out to 100 Mpc may suffice for 3%.
• Holz, D. E. & Hughes, S. A. (2005). Using gravitational-wave standard sirens. ApJ 629, 15; arXiv:astro-ph/0504616 -- the name 'standard siren'.
• Mooley, K. P. et al. (2018). Superluminal motion of a relativistic jet in the neutron-star merger GW170817. Nature 561, 355; arXiv:1806.09693 -- viewing angle about 20 degrees.
• Hotokezaka, K. et al. (2019). A Hubble constant measurement from superluminal motion of the jet in GW170817. Nature Astronomy 3, 940; arXiv:1806.10596 -- 70.3 +5.3/-5.0 (journal); 68.9 +4.7/-4.6 (arXiv).
• Dietrich, T. et al. (2020). Multimessenger constraints on the neutron-star equation of state and the Hubble constant. Science 370, 1450; arXiv:2002.11355 -- 66.2 +4.4/-4.2.
• Wang, Y.-Y. et al. (2022). arXiv:2208.09121 -- 72.57 +4.09/-4.17. Palmese, A. et al. (2023). arXiv:2305.19914 -- 75.46 +5.34/-5.39.
• Planck Collaboration (2020). Planck 2018 results VI. A&A 641, A6; arXiv:1807.06209 -- 67.4 +/- 0.5. Riess, A. G. et al. (2022). arXiv:2112.04510 -- 73.04 +/- 1.04.
• GWOSC, GW170817 strain data, CC BY 4.0 -- https://gwosc.org/eventapi/html/GWTC-1-confident/GW170817/v3/ (pinned comment).

ARCHIVE PLATES: all 11 are credited on screen in the video and listed in this project's manifest.

Absolute Magnitude takes one number the internet repeats and asks what an instrument actually returned. Every episode ends on a measured figure with its source on screen, and says plainly which part of it was converted afterwards.

No AI-generated imagery is used on this channel. Every frame of archive footage is real, publicly released material, credited on screen with its licence; every diagram is drawn in code from the numbers in the cited papers.

The chirp heard in this episode is not the detectors' recording. It is the curve that the published chirp mass predicts for the last ten seconds, computed to leading order in scripts/sonify.py.

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